math/s_clogl.c

   1 /* Compute complex natural logarithm.
   2    Copyright (C) 1997-2013 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #include <complex.h>
  21 #include <math.h>
  22 #include <math_private.h>
  23 #include <float.h>
  24
  25 /* To avoid spurious underflows, use this definition to treat IBM long
  26    double as approximating an IEEE-style format.  */
  27 #if LDBL_MANT_DIG == 106
  28 # undef LDBL_EPSILON
  29 # define LDBL_EPSILON 0x1p-106L
  30 #endif
  31
  32 __complex__ long double
  33 __clogl (__complex__ long double x)
  34 {
  35   __complex__ long double result;
  36   int rcls = fpclassify (__real__ x);
  37   int icls = fpclassify (__imag__ x);
  38
  39   if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
  40     {
  41       /* Real and imaginary part are 0.0.  */
  42       __imag__ result = signbit (__real__ x) ? M_PIl : 0.0;
  43       __imag__ result = __copysignl (__imag__ result, __imag__ x);
  44       /* Yes, the following line raises an exception.  */
  45       __real__ result = -1.0 / fabsl (__real__ x);
  46     }
  47   else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
  48     {
  49       /* Neither real nor imaginary part is NaN.  */
  50       long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x);
  51       int scale = 0;
  52
  53       if (absx < absy)
  54         {
  55           long double t = absx;
  56           absx = absy;
  57           absy = t;
  58         }
  59
  60       if (absx > LDBL_MAX / 2.0L)
  61         {
  62           scale = -1;
  63           absx = __scalbnl (absx, scale);
  64           absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L);
  65         }
  66       else if (absx < LDBL_MIN && absy < LDBL_MIN)
  67         {
  68           scale = LDBL_MANT_DIG;
  69           absx = __scalbnl (absx, scale);
  70           absy = __scalbnl (absy, scale);
  71         }
  72
  73       if (absx == 1.0L && scale == 0)
  74         {
  75           long double absy2 = absy * absy;
  76           if (absy2 <= LDBL_MIN * 2.0L)
  77             __real__ result = absy2 / 2.0L - absy2 * absy2 / 4.0L;
  78           else
  79             __real__ result = __log1pl (absy2) / 2.0L;
  80         }
  81       else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0)
  82         {
  83           long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
  84           if (absy >= LDBL_EPSILON)
  85             d2m1 += absy * absy;
  86           __real__ result = __log1pl (d2m1) / 2.0L;
  87         }
  88       else if (absx < 1.0L
  89                && absx >= 0.75L
  90                && absy < LDBL_EPSILON / 2.0L
  91                && scale == 0)
  92         {
  93           long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
  94           __real__ result = __log1pl (d2m1) / 2.0L;
  95         }
  96       else if (absx < 1.0L && (absx >= 0.75L || absy >= 0.5L) && scale == 0)
  97         {
  98           long double d2m1 = __x2y2m1l (absx, absy);
  99           __real__ result = __log1pl (d2m1) / 2.0L;
 100         }
 101       else
 102         {
 103           long double d = __ieee754_hypotl (absx, absy);
 104           __real__ result = __ieee754_logl (d) - scale * M_LN2l;
 105         }
 106
 107       __imag__ result = __ieee754_atan2l (__imag__ x, __real__ x);
 108     }
 109   else
 110     {
 111       __imag__ result = __nanl ("");
 112       if (rcls == FP_INFINITE || icls == FP_INFINITE)
 113         /* Real or imaginary part is infinite.  */
 114         __real__ result = HUGE_VALL;
 115       else
 116         __real__ result = __nanl ("");
 117     }
 118
 119   return result;
 120 }
 121 weak_alias (__clogl, clogl)